Second Edition Business Statistics COMMUNICATING W ITH NUMBERS Jaggia / Kelly BUSINESS STATISTICS jag20557_fm_i-xxxii_1.indd 29/06/15 2:43 PM jag20557_fm_i-xxxii_1.indd 29/06/15 2:43 PM Second Edition BUSINESS STATISTICS Communicating with Numbers jag20557_fm_i-xxxii_1.indd Sanjiv Jaggia Alison Kelly California Polytechnic State University Suffolk University 29/06/15 2:43 PM BUSINESS STATISTICS: COMMUNICATING WITH NUMBERS, SECOND EDITION Published by McGraw-Hill Education, Penn Plaza, New York, NY 10121 Copyright © 2016 by McGraw-Hill Education All rights reserved Printed in the United States of America Previous editions © 2013 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper DOW/DOW ISBN 978-0-07-802055-1 MHID 0-07-802055-7 Senior Vice President, Products & Markets: Kurt L Strand Vice President, General Manager, Products & Markets: Marty Lange Vice President, Content Design & Delivery: Kimberly Meriwether David Managing Director: Jame Heine Marketing Director: Lynn Breithaupt Brand Manager: Dolly Womack Director, Product Development: Rose Koos Product Developer: Christina Holt Director of Digital Content: Doug Ruby Digital Product Analyst: Kevin Shanahan Director, Content Design & Delivery: Linda Avenarius Program Manager: Mark Christianson Content Project Managers: Harvey Yep / Bruce Gin Buyer: Jennifer Pickel Design: Srdjan Savanovic Content Licensing Specialists: Keri Johnson / John Leland / Rita Hingtgen Cover Image: © Comstock/Stockbyte/Getty Images/RF; © Mitch Diamond/Photodisc/Getty Images/RF; © Mark Bowden/iStock/Getty Images Plus/Getty Images: © Rob Tringali//Getty Images; © Image Source, all rights reserved/RF; © Honqi Zhang/iStock/Getty Images Plus/Getty Images/RF; © imageBROKER/Alamy /RF; © TongRo Images/Getty Images; © Yellow Dog Productions/Digital Vision/Getty Images/RF Compositor: MPS Limited, A Macmillan Company Printer: R R Donnelley All credits appearing on page or at the end of the book are considered to be an extension of the copyright page Library of Congress Cataloging-in-Publication Data Jaggia, Sanjiv, 1960  Business statistics: communicating with numbers / Sanjiv Jaggia,   California Polytechnic State University, Alison Kelly, Suffolk University   Second Edition   pages cm.—(Business statistics)   ISBN 978-0-07-802055-1 (hardback)   Commercial statistics I Hawke, Alison Kelly II Title   HF1017.J34 2015   519.5—dc23 2015023383 The Internet addresses listed in the text were accurate at the time of publication The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites www.mhhe.com Dedicated to Chandrika, Minori, John, Megan, and Matthew v jag20557_fm_i-xxxii_1.indd 07/07/15 11:28 am A B O U T T H E AU T H O R S Sanjiv Jaggia Sanjiv Jaggia is the associate dean of graduate programs and a professor of economics and finance at California Polytechnic State University in San Luis Obispo, California After earning a Ph.D from Indiana University, Bloomington, in 1990, Dr Jaggia spent 17 years at Suffolk University, Boston In 2003, he became a Chartered Financial Analyst (CFA®) Dr Jaggia’s research interests include empirical finance, statistics, and econometrics He has published extensively in research journals, including the Journal of Empirical Finance, Review of Economics and Statistics, Journal of Business and Economic Statistics, and Journal of Econometrics Dr Jaggia’s ability to communicate in the classroom has been acknowledged by several teaching awards In 2007, he traded one coast for the other and now lives in San Luis Obispo, California, with his wife and daughter In his spare time, he enjoys cooking, hiking, and listening to a wide range of music Alison Kelly Alison Kelly is a professor of economics at Suffolk University in Boston, Massachusetts She received her B.A degree from the College of the Holy Cross in Worcester, Massachusetts; her M.A degree from the University of Southern California in Los Angeles; and her Ph.D from Boston College in Chestnut Hill, Massachusetts Dr Kelly has published in journals such as the American Journal of Agricultural Economics, Journal of Macroeconomics, Review of Income and Wealth, Applied Financial Economics, and Contemporary Economic Policy She is a Chartered Financial Analyst (CFA) and regularly teaches review courses in quantitative methods to candidates preparing to take the CFA exam Dr Kelly has also served as a consultant for a number of companies; her most recent work focuses on how large financial institutions satisfy requirements mandated by the Dodd-Frank Act She resides in Hamilton, Massachusetts, with her husband and two children vi jag20557_fm_i-xxxii_1.indd 29/06/15 2:43 PM A Unique Emphasis on Communicating with Numbers Makes Business Statistics Relevant to Students Statistics can be a fun and enlightening course for both students and teachers From our years of experience in the classroom, we have found that an effective way to make statistics interesting is to use timely business applications to which students can relate If interest can be sparked at the outset, students may end up learning statistics without realizing they are doing so By carefully matching timely applications with statistical methods, students learn to appreciate the relevance of business statistics in our world today We wrote Business Statistics: Communicating with Numbers because we saw a need for a contemporary, core statistics textbook that sparked student interest and bridged the gap between how statistics is taught and how practitioners think about and apply statistical methods Throughout the text, the emphasis is on communicating with numbers rather than on number crunching In every chapter, students are exposed to statistical information conveyed in written form By incorporating the perspective of professional users, it has been our goal to make the subject matter more relevant and the presentation of material more straightforward for students In Business Statistics, we have incorporated fundamental topics that are applicable for students with various backgrounds and interests The text is intellectually stimulating, practical, and visually attractive, from which students can learn and instructors can teach Although it is application oriented, it is also mathematically sound and uses notation that is generally accepted for the topic being covered This is probably the best book I have seen in terms of explaining concepts Brad McDonald, Northern Illinois University The book is well written, more readable and interesting than most stats texts, and effective in explaining concepts The examples and cases are particularly good and effective teaching tools Andrew Koch, James Madison University Clarity and brevity are the most important things I look for—this text has both in abundance Michael Gordinier, Washington University, St Louis WALKTHROUGH jag20557_fm_i-xxxii_1.indd B U S I N E S S S TAT I S T I C S vii 29/06/15 2:43 PM Continuing Key Features The second edition of Business Statistics reinforces and expands six core features that were well-received in the first edition Integrated Introductory Cases.  Each chapter begins with an interesting and relevant introductory case The case is threaded throughout the chapter, and it often serves as the basis of several examples in other chapters Writing with Statistics.  Interpreting results and conveying information effectively is critical to effective decision making in a business environment Students are taught how to take the data, apply it, and convey the information in a meaningful way Unique Coverage of Regression Analysis.  Relevant coverage of regression without repetition is an important hallmark of this text Written as Taught.  Topics are presented the way they are taught in class, beginning with the intuition and explanation and concluding with the application Integration of Microsoft Excel®.  Students are taught to develop an understanding of the concepts and how to derive the calculation; then Excel is used as a tool to perform the cumbersome calculations In addition, guidelines for using Minitab, SPSS, and JMP are provided in chapter appendices; detailed instructions for these packages and for R are available in Connect Connect® Business Statistics.  Connect is an online system that gives students the tools they need to be successful in the course Through guided examples and LearnSmart adaptive study tools, students receive guidance and practice to help them master the topics I really like the case studies and the emphasis on writing We are making a big effort to incorporate more business writing in our core courses, so that meshes well Elizabeth Haran, Salem State University For a statistical analyst, your analytical skill is only as good as your communication skill Writing with statistics reinforces the importance of communication and provides students with concrete examples to follow Jun Liu, Georgia Southern University viii    B U S I N E S S S T A T I S T I C S    WALKTHROUGH    Features New to the Second Edition The second edition of Business Statistics features a number of improvements suggested by numerous reviewers and users of the first edition First, every section of every chapter has been scrutinized, and if a change would enhance readability, then that change was made In addition, Excel instructions have been streamlined in every chapter We feel that this modification provides a more seamless reinforcement for the relevant topic For those instructors who prefer to omit the Excel parts, these sections can be easily skipped Moreover, most chapters now include an appendix that provides brief instructions for Minitab, SPSS, and JMP More detailed instructions for Minitab, SPSS, and JMP can be found in Connect Dozens of applied exercises of varying levels of difficulty have been added to just about every section of every chapter Many of these exercises include new data sets that encourage the use of the computer; however, just as many exercises retain the flexibility of traditional solving by hand Both of us use Connect in our classes In an attempt to make the technology component seamless with the text itself, we have reviewed every Connect exercise In addition, we have painstakingly revised tolerance levels and added rounding rules The positive feedback from users due to these adjustments has been well worth the effort In addition, we have included numerous new exercises in Connect We have also reviewed every probe from LearnSmart Instructors who teach in an online or hybrid environment will especially appreciate these modifications Here are some of the more noteworthy, specific changes: • Some of the Learning Outcomes have been rewritten for the sake of consistency • In Chapter (Numerical Descriptive Measures), the discussion of the weighted mean occurs in Section 3.1 (Measures of Central Location) instead of Section 3.7 (Summarizing Grouped Data) Section 3.6 has been renamed from “Chebyshev’s Theorem and the Empirical Rule” to “Analysis of Relative Location”; in addition, we have added a discussion of z-scores in this section • In Chapter (Introduction to Probability), the term a priori has been replaced by classical • In Chapter (Discrete Probability Distributions), the use of graphs now complements the discussion of the binomial and Poisson distributions • In Chapter (Sampling and Sampling Distributions), the standard error of a statistic is now denoted as “se” instead the standard error of the sample of “SD.” For instance, mean is now denoted as se(X) instead of SD(X) • The discussion of the properties of estimators has been moved from Section 8.1 to an appendix in Chapter • In Section 16.1 (Polynomial Models), the discussion of the marginal effects of x on y has been expanded • In Section 17.1 (Dummy Variables), there is now an example of how to conduct a hypothesis test when the original reference group must be changed • In Chapter 18 (Time Series Forecasting), the data used for the “Writing with Statistics” example has been revised WALKTHROUGH jag20557_fm_i-xxxii_1.indd B U S I N E S S S TAT I S T I C S ix 29/06/15 2:43 PM www.downloadslide.net Test of joint significance In regression analysis, a test to determine whether the explanatory variables have a joint statistical influence on the response variable; it is often regarded as a test of the overall usefulness of a regression model Unconditional probability The probability of an event without any restriction Test of linear restrictions In regression analysis, a test to determine if the restrictions specified in the null hypothesis are invalid Unrestricted model A regression model that imposes no restrictions on the coefficients Test Statistic A sample-based measure used in hypothesis testing Unsystematic patterns In time series, patterns caused by the presence of a random error term Time series over time Unweighted aggregate price index An aggregate price index based entirely on aggregate prices with no emphasis placed on quantity A set of sequential observations of a variable Time series data over time Values of a characteristic of a subject Total probability rule A rule that expresses the unconditional probability of an event, P(A), in terms of probabilities conditional on various mutually exclusive and exhaustive events The total probability rule conditional on two events B and Bc is P(A) = P(A ∩ B) + P(A ∩ Bc) = P(A ∣ B)P(B) + P(A ∣ Bc)P(Bc) Total sum of squares (SST) In regression analysis, it measures the total variation in the response variable It can be decomposed into explained and unexplained variations Trend The trend refers to a long-term upward or downward movement of a time series Tukey’s honestly significant differences (HSD) method In ANOVA, a test that determines which means significantly differ by comparing all pairwise differences of the means Two-tailed hypothesis test A test in which the null hypothesis can be rejected on either side of the hypothesized value of the population parameter Two-tailed test In hypothesis testing, when the null hypothesis is rejected if the value of the test statistic falls in either the left tail or the right tail of the distribution Two-way ANOVA test A test that simultaneously examines the effect of two factors on the mean Two-way ANOVA test with interaction A two-way ANOVA test that captures the possible relationship between the two factors Two-way ANOVA tests without interaction A two-way ANOVA test that does not capture the possible relationship between the two factors Type I error In a hypothesis test, this error occurs when the decision is to reject the null hypothesis when the null hypothesis is actually true Type II error In a hypothesis test, this error occurs when the decision is to not reject the null hypothesis when the null hypothesis is actually false U Unbalanced data A completely randomized ANOVA design where the number of observations are not the same for each sample Unbiased An estimator is unbiased if its expected value equals the unknown population parameter being estimated G-8 jag20557_gloss_G1-G8.indd B U S I N E S S S TAT I S T I C S Union The union of two events A and B, denoted A ∪ B, is the event consisting of all outcomes in A or B Upper control limit In a control chart, the upper control limit indicates excessive deviation above the expected value of the variable of interest V Variable A general characteristic being observed on a set of people, objects, or events, where each observation varies in kind or degree Variance The average of the squared differences from the mean; a common measure of dispersion W Wald-Wolfowitz runs test A nonparametric test to determine whether the elements in a sequence appear in a random order Weighted aggregate price index An aggregate price index that gives higher weight to the items sold in higher quantities Weighted mean When some observations contribute more than others in the calculation of an average Wilcoxon rank-sum test A nonparametric test to determine whether two population medians differ under independent sampling Also known as the Mann-Whitney test Wilcoxon signed-rank test A nonparametric test to determine whether a sample could have been drawn from a population having a hypothesized value as its median; this test can also be used to determin whether the median difference differs from zero under matched-pairs sampling Within-treatments variance In ANOVA, a measure of the variability within each sample X x chart A control chart that monitors the central tendency of a production process Z z-score The relative position of a value within a data set; it is also used to detect outliers z  table A table providing cumulative probabilities for positive or negative values of the standard normal random variable Z GLOSSARY 29/06/15 4:02 PM PHOTO CREDITS Chapter Chapter 14 Chapter1 Opener: © Chris Hondros/Getty Images News/Getty Images; p 247:  © Joe Raedle/ Getty Images News/Getty Images; p 257: © Ryan McVay/Photodisc/Getty Images RF Opener: © Blend Images-JGI/Jamie Grill/ Band X Pictures/Getty Images RF; p 503: © David J Phillip/AP Images; p 506: © Kick Images/Photodisc/Getty Images RF Chapter Chapter 15 Opener: © Uli Deck/picture-alliance/dpa/AP Images; p.289: © McGraw-Hill Companies, Inc Mark Dierker, photographer RF; p 291(left): © The McGraw-Hill Companies, Inc./Andrew Resek, photographer RF; p 291(right): © Paul Sakuma/AP Images Opener: © Rob Tringali/MLB Photos via Getty Images; p 523: © Mark Cunningham/ MLB Photos via Getty Images; p 546: © Elsa/Getty Images Sport/ Getty Images Opener: © Randy Lincks/All Canada Photos/Getty Images; p 7: © Comstock/ Stockbyte/Getty Images RF; p 9: © Agencja Fotograficzna Caro/Alamy Stock Photo; p 13: © Dennis Welsh/UpperCut Images/ Getty Images RF Chapter Opener: © Mitch Diamond/Photodisc/Getty Images RF; p 18: © sbk_20d pictures/ Moment/Getty Images RF; p 37: © Brand X Pictures/Stockbyte/Getty Images Plus/ Getty Images RF; p 47: © rubberball// Getty Images RF Chapter Opener: © Mark Bowden/iStock/Getty Images Plus/Getty Images RF; p 64: © Sebastian Pfeutze/Taxi/Getty Images; p 81: © Ingram Publishing RF; p 96: © Mike Watson Images/moodboard/Getty Images Plus/Getty Images RF Chapter Chapter Opener: © Ken Seet/Corbis Images/ SuperStock RF; p 322: © Asia Images Group/Getty Images RF; p 330: © Ariel Skelley/Blend Images LLC RF Chapter 10 Opener: © John Smock/SIPA/Newscom; p 356: © Chris Hondros/Getty Images News/Getty Images; p 366(top): © JGI/ Blend Images LLC RF; p 366(bottom): © STOCK4B-RF/Getty Images RF Opener: © Fab Fernandez/Image Source/ Getty Images RF; p 114: © Gene J Puskar/ AP Images; p 129: © Digital Vision/ Photodisc/Getty Images RF; p 141: © Rolf Bruderer/Blend Images/Getty Images RF Chapter 11 Chapter Chapter 12 Opener: © Jewel Samad/AFP/Getty Images; p 177: © Bubbles Photolibrary/ Alamy; p 182: © Image Source/Getty Images RF Chapter Opener: © Vision SRL/Photodisc/Getty Images RF; p 210: © Natalia Lisovskaya/ Shutterstock; p 220: © Image Source, all rights reserved RF Opener: © Hero Images/Getty Images RF; p 391: © Spencer Grant/PhotoEdit—All rights reserved.; p 394: © Gerry Broome/ AP Images Opener: © Hongqi Zhang/iStock/Getty Images Plus/Getty Images RF; p 414: © Jean Baptiste Lacroix/WireImage/Getty Images; p 422: © JGI/Blend Images/Getty Images RF Chapter 13 Opener: © Jorge Garrido/Alamy; p 447: © PBNJ Productions/Getty Images; p 464: © Mitchell Funk/Photographer’s Choice/Getty Images Chapter 16 Opener: © Yellow Dog Productions/Digital Vision/Getty Images RF; p 575: © Patrick Cooper/Shutterstock; p 578: © Photodisc/ Getty Images RF Chapter 17 Opener: © Asia Images Group/Getty Images RF; p 603: © Tom Stewart/Corbis/Getty Images; p 613: © Mark J Terrill, Pool/ AP Images Chapter 18 Opener: © Pietro Scozzari/age fotostock; p 647: © David Paul Morris/Bloomberg via Getty Images; p 653: © Evan Vucci/AP Images Chapter 19 Opener: © imageBROKER/Alamy RF; p 674: © Peter Titmuss/Alamy; p 681: © Bettmann/Getty Images Chapter 20 Opener: © monkeybusinessimages/iStock/ Getty Images Plus/Getty Images RF; p 709: © Ken Reid/Photographer’s Choice/ Getty Images; p 719: © gkrphoto/Getty Images PC-1 CREDITS www.downloadslide.net www.downloadslide.net jag20557_credit_PC1-PC2.indd 29/06/15 3:30 PM www.downloadslide.net Acceptance sampling, 251 Addition rule, 117–118 Adidas, 107, 126, 127, 403, 411, 414 Adjusted closing price, 665–666 Adjusted coefficient of determination, 502–503, 638 Adjusted seasonal index, 642–643 Aggregate price indices, 670 unweighted, 670–671 weighted, 671–673 Akiko Hamaguchi, 191, 210 Alpha, 519 Alstead, Troy, Alternative hypotheses, 302, 303–305 American Public Transportation Association, 447 Analysis of variance (ANOVA); see also One-way ANOVA; Two-way ANOVA ANOVA table, 437 defined, 434 uses of, 432, 434 Annualized return, 73–74 ANOVA; see Analysis of variance; One-way ANOVA; Two-way ANOVA ANOVA table, 437 Anti-log function, 567 Arithmetic mean, 60–61, 74 Arizona Cardinals, 114 Asset returns; see Returns Assets; see Portfolios Assignable variation, 252 Associated Press, 330 Asymptotic distributions, 196 Autoregressive models, 650 Average growth rates, 74–75 Average study time, hypothesis tests, 301, 322 Averages; see Mean B Balanced data, 444 Bar charts, 19, 21–22 Barnes, Valerie, 681 Bayes, Thomas, 134 Bayes’ theorem, 131, 134–136 BEA; see Bureau of Economic Analysis Beane, Jared, 269, 270, 289 Bell curve, 196; see also Symmetric distributions Bell Telephone Laboratories, 252 Bell-shaped distribution, 86 Bernoulli, James, 166 Bernoulli process, 166, 404 Beta, 519 Between-treatments estimate of population variance, 435–436 Between-treatments variance, 435 Bias, 232 Binary choice models defined, 606 linear probability model, 606–607, 608 logit model, 607–609 Binomial experiments, 166–169, 404 Binomial probability distributions constructing, 166–168 defined, 166 with Excel, 171 formula, 168–169 normal approximation, 209 sampling distribution of sample proportion, 244 Binomial random variable defined, 166, 168 expected values, 169 standard deviation, 169 variance, 169 Blocked outcomes, 451 Bloomberg Businessweek, 247 BLS; see Bureau of Labor Statistics Bonds; see Returns Boston Celtics, 613 Boston Globe poll, Box plots, 70–71 Box-and-whisker plot, 70–71 Brewery, Guinness, 277 Brown, Scott, 4, 235–236 Bryant, Kobe, 613 Bureau of Economic Analysis (BEA), Bureau of Labor Statistics (BLS), 6, 7, 677 Business cycles, 640 INDEX A C c chart, 252 Capital asset pricing model (CAPM), 519–529 Capital gains yields, 664 CAPM; see Capital asset pricing model Causal forecasting models, 624, 650–651 Causation, correlation and, 5, 481 Census Bureau, U.S., 7, 61 Centered moving average (CMA), 641–642 Centerline, 252 Central limit theorem (CLT) sampling distribution of sample mean, 240–241 sampling distribution of sample proportion, 245 Central location measures arithmetic mean, 60–61, 74 defined, 60 Excel calculations, 64–67 geometric mean, 73–75 median, 61–63 mode, 63–64 weighted mean, 66, 90 Chance variation, 251–252 Charts; see Control charts; Graphical displays Chebyshev, Pavroty, 85 Chebyshev’s theorem, 85–86, 87 Chi-square distribution characteristics, 376–377 defined, 376 degrees of freedom, 376–377 locating values and probabilities, 377–379 Chi-square table, 378 I-1 jag20557_index_I1-I22.indd 08/07/15 2:22 pm www.downloadslide.net Chi-square tests goodness-of-fit for independence, 410–414 for multinomial experiments, 404–408 for normality, 416–418 Jarque-Bera, 419 Classes, 25–27, 28 Classical probability, 113 Clinton, Hillary, 234 CLT; see Central limit theorem Cluster sampling, 235 Clusters, 235 CMA; see Centered moving average Coakley, Martha, 4, 235–236 Coefficient of determination, 500–502, 574 Coefficient of variation (CV), 80 Combination formula, 139 Complement, of event, 110, 117 Complement rule, 117 Conditional probability, 119–120, 134 Confidence coefficient, 272 Confidence intervals defined, 270 for differences in means, 340–342 individual significance tests, 516–519 interpreting, 272 margin of error, 270–271, 287, 288 for mean difference, 351–352 misinterpretation, 272 of population mean with known standard deviation, 271–275 with unknown standard deviation, 277–281 of population proportion, 284–285, 288–289 of population variance, 379–380 for population variance ratio, 388 predicted values, 532–533 for proportion differences, 360–361 sample sizes and, 287–289 two-tailed hypothesis tests, 315–316 using Excel, 275, 281 width and precision, 273–274 Constants, 237 Consumer Price Index (CPI), 670, 677–678, 681; see also Inflation rates; Price indices Consumers, risk and, 159–160 Contingency tables chi-square tests, 410–411 defined, 126, 410 using, 126–129 Continuous probability distributions; see also Normal distribution exponential, 213–215 lognormal, 216–218 uniform, 193 Continuous random variables, 9, 152, 192 Continuous uniform distribution, 193 Continuous variables, Control charts defined, 252 I-2 jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S _ p charts, 252, 254–255 for qualitative data, 252, 254–255 for quantitative data, 252, 253–254 _ x charts, 252 Control variables; see Explanatory variables Correlation causation and, 5, 481 spurious, 5, 481 Correlation analysis hypothesis tests, 480 limitations of, 481 Correlation coefficient calculating, 94 defined, 93 hypothesis tests, 480 population, 93, 480 of portfolio returns, 164 sample, 93, 479 Spearman rank, 707 Correlation-to-causation fallacy, Counting rules combination formula, 139 factorial formula, 138 permutation formula, 139 Covariance calculating, 94 defined, 92 population, 92 of portfolio returns, 164 sample, 92, 478 Cox, Sean, 433, 447 CPI; see Consumer Price Index Critical values defined, 312 four-step procedure and, 314 hypothesis testing, 312–315 Cross-sectional data, 6, Cubic regression model, 563–564 predictions, 563 Cubic trend models, 638 Cumulative distribution function, 153, 154, 192 Cumulative frequency distribution defined, 28 ogives, 35 Cumulative relative frequency distributions, 29 Curvilinear relationships, 44; see also Polynomial regression models CV; see Coefficient of variation Cyclical patterns, 626, 640 D Data; see also Time series data; Variables cross-sectional, 6, measurement scales, 9–12 sources, standardizing, 87 types, 6–7 websites, Deciles INDEX 08/07/15 2:22 pm www.downloadslide.net Decision rules critical value approach, 312, 313 p -value approach, 309, 310 Decomposition analysis, 640–641 extracting seasonality, 641–643 extracting trend, 643–644 forecasting, 644–645 Deflated time series, 676–678 Degrees of freedom (df), 278 Dependent events, 121 Dependent variable; see Response variable Descriptive statistics, Detection approach, 251 Deterministic relationships, 484 df; see Degrees of freedom Discrete choice models; see Binary choice models Discrete probability distributions, 153–156 binomial constructing, 166–168 defined, 166 with Excel, 171 formula, 168–169 sampling distribution of sample proportion, 244 discrete uniform distribution, 155 graphical displays, 154 hypergeometric, 178–180 Poisson, 173–176 properties of, 154 Discrete random variables, 8–9, 152, 153 expected value, 158 standard deviation, 158 variance, 158 Discrete uniform distribution, 155 Discrete variables, 8–9 Dispersion measures, 77 coefficient of variation, 80 Excel calculations, 80–81 mean absolute deviation, 77–78 range, 77 standard deviation, 78–79, 85–88 variance, 78–79 Distribution-free tests; see Nonparametric tests DJIA; see Dow Jones Industrial Average Dow Jones Industrial Average (DJIA), Dummy variable trap, 594 Dummy variables defined, 590 interaction variables and, 599–603 for multiple categories, 593–596 seasonal, 640, 645–647 significance tests, 592, 600 use of, 590 Duracel, E The Economist, Edwards, Matthew, 17 Empirical probability, 112, 113 Empirical rule, 86–87, 202–204 Endogeneity, 537 Error sum of squares (SSE) ordinary least squares, 486 in two-way ANOVA, 452–453, 460 within-treatments estimate of population variance, 436 Errors; see also Margin of error; Standard error random, 626 Type I errors, 305–306 Type II errors, 305–306 espn.com, Estimates, 237 Estimation; see Confidence intervals; Maximum likelihood estimation (MLE) Estimators, 237 Events complement of, 110, 117 defined, 108, 109 dependent, 121 exhaustive, 109 independent, 121, 123 intersection of, 109–110 mutually exclusive, 109, 119 probabilities, 108–110 union of, 109, 110, 117 Excel ANOVA problems, 437–439 bar charts, 21–22 central location measures, 64–67 chi-square tests, 406–408 confidence intervals, 275, 281 control charts, 255 correlation coefficient, 94, 480 covariance, 94, 480 dispersion measures, 80–81 exponential distribution, 215 exponential smoothing, 631 histogram, 31–33 hypergeometric probabilities, 180 hypothesis testing, 316–317 hypothesis tests for differences in means, 344–346 hypothesis tests for mean difference, 354–355 lognormal distribution, 218 moving averages, 631 multiple regression, 493–494 normal distribution, 209 ogives, 36 pie charts, 21 Poisson probabilities, 176 polygon, 34–35 p-values, 321–322, 382, 390–391 regression statistics, 499–500 residual plots, 538 sample regression equation, 488–489 scatterplots, 45, 486–488 smoothing techniques, 631 standard error of the estimate, 499–500 trendlines, 486–488 two-way ANOVA with interaction, 460–461 no interaction, 453–455 INDEX jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S I-3 08/07/15 2:22 pm www.downloadslide.net Exhaustive events, 109 Expected frequencies, 411–413 Expected portfolio returns, 163–164 Expected return of the portfolio, 163 Expected value, 158 Experiments; see also Events binomial, 166–169, 404 defined, 108 multinomial, 404–408 outcomes, 108 Explained variation, 500 Explanatory variables; see also Dummy variables assumption and, 544 defined, 483 multicollinearity, 540–541 in multiple regression, 492 qualitative, 590 quantitative, 590 in simple linear regression, 483 Exponential function, 567 Exponential model, 569, 570–574, 571 Exponential probability distribution, 213–215 Exponential smoothing, 628–631 Exponential trend models, 634–637 estimating, 634–635 formula, 635 with seasonal dummy variables, 646 F F distribution characteristics, 385–386 locating values and probabilities, 386–387 F table, 386–387 F test one-tailed, 521 partial, 527–530 Factorial formula, 138 Fahrenheit scale, 12 Farnham, Matthew, 506 Federal Reserve, 106 Federal Reserve Economic Data (FRED), Fidelity Investments, 59, 81, 375, 391, 687 Finite population correction factor, 248–250 Fisher, Irving, 666 Fisher equation, 666 Fisher’s least significant difference (LSD) method, 442–444, 445, 455 Fitted value, 625 Forecasting; see also Smoothing techniques causal models, 624, 650–651 decomposition analysis, 644–645 model selection, 625 noncausal models, 624 qualitative, 624 quantitative, 624 trend models exponential, 634–637 linear, 633–634, 645 polynomial, 637–638 quadratic, 637–638 I-4 jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S Fortune, Fraction defective charts, 254 FRED; see Federal Reserve Economic Data Frequencies, expected, 411–413 Frequency distributions classes, 25–27, 28 constructing, 26–27 cumulative, 28 defined, 28 graphical displays charts, 19–23 histograms, 30–33 ogives, 35–36 polygons, 33–35 qualitative data, 18–23 quantitative data, 25–36 relative, 19, 29 G Gallup Poll, Geometric mean, 73–75 Geometric mean return, 73–74 Goodness-of-fit tests adjusted coefficient of determination, 502–503 coefficient of determination, 500–502 for independence, 410–414 for multinomial experiments, 404–408 for normality, 416–418 for regression analysis, 497 standard error of the estimate, 497–500 Google, Gossett, William S., 277 Grand mean, 435 Graphical displays bar charts, 19, 21–22 box plot, 70–71 guidelines, 22–23 histograms, 30–33 ogives, 35–36 pie charts, 19–21 polygons, 33–35 residual plots, 537 scatterplots, 43–46, 478, 486–488 stem-and-leaf diagrams, 41–43 Great Depression, 232 Grouped data, summarizing, 89–91 Growth rates, average, 74–75 H Heteroskedasticity, 537 Histograms constructing, 31–33 defined, 30 relative frequency, 30 shapes, 31 Hoover, Herbert, 232 HSD; see Tukey’s honestly significant differences method Hypergeometric probability distributions, 178–180 INDEX 08/07/15 2:22 pm www.downloadslide.net Hypergeometric random variables, 179 Hypotheses alternative, 302, 303–305 null, 302, 303–305 Hypothesis tests; see also Analysis of variance; Nonparametric tests for correlation coefficient, 480 for differences in means, 342–344 of individual significance, 516–519 interpreting results, 317 of joint significance, 521–522 left-tailed, 303, 314 for mean difference, 352–354 one-tailed, 303–305 of population mean, with known standard deviation, 307–317 critical value approach, 312–315 p-value approach, 308–312 of population mean, with unknown standard deviation, 319–322 of population median, 690 of population proportion, 325–328 for population variance, 380–381 for population variance ratio, 388–390 for proportion differences, 361–363 rejecting null hypothesis, 302–303 right-tailed, 303, 314 significance level, 309 two-tailed, 303–305, 314, 315–316 Type I and Type II errors, 305–306 using Excel, 316–317 In-sample criteria, 625 Instrumental variables, 544 Interaction variables, 599–603 Interquartile range (IQR), 71, 77 Intersection, of events, 109–110 Interval, 270 Interval estimate, 270; see also Confidence intervals Interval estimates, 532–535 Interval scale, 12 Inverse transformation, 207–209 Investment returns; see also Returns calculating, 664 income component, 664 price change component, 664 IQR; see Interquartile range I L IBM, Iced coffee, 247 Income yields, 664 Independence, chi-square test for, 410–414 Independent events, 121, 123 Independent random samples defined, 340 Wilcoxon rank-sum test, 693 Index numbers; see also Indices base periods, 668 defined, 668 Indicator variables; see Dummy variables Indices; see also Price indices base periods, 668 seasonal adjusted, 642–643 unadjusted, 642 Individual significance, tests of, 516–519 Inferential statistics, Inflation; see also Price indices effects, 676, 677 returns and, 666 Inflation rates calculating, 678–679 defined, 678 expected, 666 J Jarque-Bera test, 419 Johnson, Rebecca, 687 Johnson & Johnson, 520 Joint probability, 128 Joint probability table, 128 Joint significance, tests of, 521–522 Jones, Anne, 151 K Kennedy, Ted, 4, 235 Knight, Susan, 301 Kruskal-Wallis test, 701–703 test statistics, 702 Kurtosis, 66 Kurtosis coefficients, 419 Lagged regression models, 650–651 Landon, Alf, 232 Laspeyres price index, 671–672, 673 Law of large numbers, 113 LCL; see Lower control limit Leach, Ben, 546 Left-tailed hypothesis, 303, 314 Linear probability model (LPM), 606–607, 608 Linear relationships; see also Multiple regression model; Simple linear regression model correlation coefficient, 93, 479, 481 covariance, 92, 478 multicollinearity, 540–541 negative, 92 positive, 92 sample regression equation, 485–486 scatterplots, 44, 478, 486–488 slopes, 484 Linear restrictions, general test of, 527–530 Linear trend models forecasts, 633–634 formula, 633 with seasonal dummy variables, 645 Literary Digest polls, 232–233 Little Ginza, 191, 210 Logarithmic model, 569–570, 571 INDEX jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S I-5 08/07/15 2:22 pm www.downloadslide.net Logarithms exponential model, 569, 570–574, 571 logarithmic model, 569–570, 571 log-log model, 567–569, 571 natural, 567 semi-log model, 569, 571 Logit model, 607–609 Log-log model, 567–569, 571 Lognormal distribution, 216–218 Los Angeles Lakers, 613 Lower control limit (LCL), 252–253 LPM; see Linear probability model LSD; see Fisher’s least significant difference method M MAD; see Mean absolute deviation Main effects, 461 Major League Baseball (MLB), 515, 523, 546 Mann-Whitney test; see Wilcoxon rank-sum test Margin of error, confidence interval, 270–271, 287, 288 Marginal probability, 128 Matched outcomes, 451 Matched-pairs sampling mean difference, 351–355 recognizing, 351 Wilcoxon signed-rank test, 355, 694 Matthews, Robert, 481 Maximum likelihood estimation (MLE), 608 McCaffrey, Luke, McDonald’s, 213 Mean; see also Population mean; Sample mean arithmetic, 60–61, 74 for frequency distribution, 89–91 geometric, 73–75 moving average, 626–628 weighted, 66, 90 Mean absolute deviation (MAD), 77–78 forecasting models and, 625 Mean difference confidence intervals, 351–352 hypothesis test, 352–354 matched-pairs experiments, 351–355 Mean square error (MSE), 436, 460, 521 forecasting models, 625 Mean square for factor A (MSA), 452, 459 Mean square for factor B (MSB), 452, 459 Mean square for interaction (MSAB), 460 Mean square for treatments (MSTR), 435 Mean square regression (MSR), 521 Mean-variance analysis, 83–84 Measurement scales, interval, 12 nominal, 9–10, 18 ordinal, 10–12, 18 ratio, 12 Median, 61–63; see also Population median calculating, 62–63 defined, 61 Method of least squares; see Ordinary least squares (OLS) Method of runs above and below median, 716 I-6 jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S Michigan State University, 681 Microsoft Corporation, 664 MLB; see Major League Baseball MLE; see Maximum likelihood estimation Mode, 63–64 Model selection, for forecasting, 625 Moving average methods, 626–628, 631 m-period moving average, 626–628 MSA; see Mean square for factor A MSAB; see Mean square for interaction MSB; see Mean square for factor B MSE; see Mean square error MSR; see Mean square regression MSTR; see Mean square for treatments Multicollinearity, 537, 540–541 Multinomial experiments, 404 Multiple R, 502 Multiple regression model; see also Regression analysis defined, 492 explanatory variables, 492 interval estimates for predictions, 532–535 response variable, 492 sample regression equation, 492–493 test of linear restrictions, 527–530 tests of individual significance, 516–519 tests of joint significance, 521–522 Multiplication rule, 122–123 Mutually exclusive events, 109, 119 N n factorial, 138 Nasdaq; see National Association of Securities Dealers Automated Quotations National Association of Securities Dealers Automated Quotations (Nasdaq), National Basketball Association (NBA), 613 Natural logarithms, 567 NBA; see National Basketball Association Negatively skewed distributions, 31, 66 New York Stock Exchange (NYSE), 9–10, 624 The New York Times, Nike, Inc., 107, 126, 127, 128, 403, 411, 414, 623, 641, 644–645, 647 Nominal returns, 666; see also Returns Nominal scale, 9–10, 18 Nominal terms, 676 Noncausal models, 624 Nonlinear models; see Polynomial regression models Nonparametric tests compared to parametric tests, 688, 708 disadvantages, 688 Kruskal-Wallis test, 701–703 sign test, 711–713 Spearman rank correlation test, 705–708 Wilcoxon rank-sum test, 346, 355, 694–698 Wilcoxon signed-rank test for matched-pairs sample, 694–695 for population median, 688–692 software, 698 Nonresponse bias, 233 INDEX 08/07/15 2:22 pm www.downloadslide.net Normal curve, 197 Normal distribution characteristics, 196–197 defined, 193 empirical rule, 86–87, 202–204 of error term, 537 probability density function, 196–197 standard, 198 using Excel, 209 Normal transformation, 205–207 Normality goodness-of-fit test, 416–418 Jarque-Bera test, 419 Null hypotheses, 302, 303–305; see also Hypothesis tests defined, 302 formulating, 303 rejecting, 302–303 Type I and Type II errors, 305–306 NYSE; see New York Stock Exchange O Obama, Barack, 5, 234 Objective probabilities, 113 Odds ratios, 114 Ogives, 35–36 Ohio State University, OLS; see Ordinary least squares One-tailed hypothesis, 303–305 One-way ANOVA between-treatments estimate, 435–436 defined, 434 samples, 434 test statistic, 436 within-treatments estimate, 435, 436–437 Ordinal scale, 10–12, 18 Ordinary least squares (OLS) lines fit by, 486 normal distribution, 516 properties, 537 Outliers, 61 Out-of-sample criteria, 625 P Paasche index, 672, 673 Parameters; see Population parameters Parametric tests; see also F test; t test assumptions, 688 compared to nonparametric tests, 688, 708 Partial F test, 527–530 _ p charts, 252, 254–255 Pearson correlation coefficient; see Correlation coefficient Percent defective chart, 254 Percent frequencies, 19 Percentiles box plot, 70–71 calculating, 69–70 defined, 69 Permutation formula, 139 Pie charts, 19–21 Pinnacle Research, 269 Pittsburgh Steelers, 114 Poisson, Simeon, 173 Poisson probability distribution, 173–176 Poisson process, 174 Poisson random variables, 173, 174–176 Polls, 5, 232–233, 234–235 Polygons, 33–35 defined, 33 Polynomial regression models cubic, 563–564 defined, 563 quadratic compared to linear model, 558–563 formula, 558 predictions, 558 Polynomial trend models, 637–638 Pooled estimates, 341 Population defined, 5, 232 samples and, 6, 232 Population coefficient of variation, 80 Population correlation coefficient, 93, 480 Population covariance, 92 Population mean, 158 confidence intervals of differences, 340–342 with known standard deviation, 271–275 with unknown standard deviation, 277–281 differences between confidence intervals, 340–342 Fisher’s LSD method, 442–444, 445, 455 hypothesis test, 342–344 test statistic, 343 Tukey’s HSD method, 442, 444–446, 455 expected value, 158 formula, 60 matched-pairs experiments, 351 Population mean absolute deviation, 78 Population median Kruskal-Wallis test, 701–703 matched-pairs experiments, 694–695 Wilcoxon rank-sum test, 346, 355, 695–698 Wilcoxon signed-rank test for matched-pairs sample, 694–695 for population median, 694–695 software, 698 Population parameters constants, 237 defined, inferences about, 6, 232, 237 mean as, 61 Population proportion confidence intervals, 284–285, 288–289 differences between applications, 359–360 confidence intervals, 360–361 hypothesis test, 361–363 test statistic, 362 hypothesis tests, 325–328 INDEX jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S I-7 08/07/15 2:22 pm www.downloadslide.net Population standard deviation, 79 Population variance between-treatments estimate, 435–436 confidence intervals, 379–380 formula, 79 hypothesis test, 380–381 quality control studies, 376 ratio between confidence intervals, 388 estimating, 385 hypothesis test, 388–390 test statistic, 389 test statistic, 380 within-treatments estimate, 435, 436–437 Portfolio returns; see also Returns correlation coefficient, 164 covariance, 164 expected, 163–164 standard deviation, 164 variance, 163–164 Portfolio risk, 164 Portfolio weights, 163 Portfolios, defined, 162 Positively skewed distributions, 31, 66 Posterior probability, 134 PPI; see Producer price index Precision, confidence intervals, 274 Predicted value, 625 Prediction intervals, 532, 535 Predictions cubic regression model, 563 quadratic regression model, 558 Predictor variables; see Explanatory variables Price indices; see also Inflation rates aggregate, 670 unweighted, 670–671 weighted, 671–673 base periods, 668 base values, 668 CPI, 670, 677–678, 681 deflated time series, 676–678 Laspeyres, 671–672, 673 Paasche, 672, 673 PPI, 670, 677–678 simple, 668 Prices adjusted closing price, 665–666 capital gains yields, 664 Prior probability, 134 Probabilities assigning, 111–113 classical, 113 concepts, 108–114 conditional, 119–120, 134 defined, 108 empirical, 112, 113 joint, 128 marginal, 128 objective, 113 I-8 jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S odds ratios, 114 posterior, 134 prior, 134 properties, 111 rules (see Probability rules) subjective, 111, 113 unconditional, 120, 134 Probability density function, 153, 192 Probability distributions, 153 continuous (see Continuous probability distributions) discrete (see Discrete probability distributions) Probability mass function, 153 Probability rules, 117–123 addition rule, 117–118 complement rule, 117 multiplication rule, 122–123 total, 131–134, 136 Probability tree, 132, 166, 168 Producer price index (PPI), 670, 677–678; see also Price indices Proportion; see Population proportion; Sampling distribution of sample proportion p-values defined, 308 four-step procedure and, 311 hypothesis testing, 308–312, 382 Q Quadratic regression model compared to linear model, 558–563 formula, 558 predictions, 558 Quadratic trend models, 637–638 Qualitative forecasting, 624; see also Forecasting Qualitative response models; see Binary choice models Qualitative variables; see also Binary choice models; Dummy variables; Population proportion contingency tables, 126–129 control charts, 254–255 defined, frequency distributions, 18–23 graphical displays, 19–23 nominal, 9–10, 18 ordinal, 10–12, 18 in regression, 590 Quality control; see Statistical quality control Quantitative forecasting, 624; see also Forecasting Quantitative variables control charts, 252, 253–254 defined, frequency distributions, 25–36 interval, 12 ratio, 12 in regression, 590 summarizing, 25–26 R R chart, 252 Random (irregular) error, 626 INDEX 08/07/15 2:22 pm www.downloadslide.net Random samples for ANOVA, 434 independent defined, 340 simple, 233–234 stratified, 234–235 Random variables binomial, 166, 168 continuous, 9, 152, 192 defined, 152 discrete, 8–9, 152 exponential, 213–219 hypergeometric, 179 lognormal, 216–217 normal transformation, 205–207 numerical outcomes and, 153 Poisson, 173, 174–176 properties of, 162 Randomized block designs, 451 Ranges defined, 77 interquartile, 71, 77 Ratio scale, 12 Ratio-to-moving average, 642 Reagan, Ronald Wilson, 681–682 Real returns, 666 Real terms, 676 Regression analysis, 483; see also Multiple regression model; Simple linear regression model assumptions, 537–538 comparing models, 574–575 goodness-of-fit tests, 497 qualitative variables, 590 quantitative variables, 590 reporting results, 522–523 violations of assumptions, 540–544 Rejection region, 312 Relative frequency distribution cumulative, 29 qualitative data, 19 quantitative data, 29 summarizing, 91 Residual plots, 537 Residuals model selection criteria, 625 in simple linear regression, 485 Response variable binary choice models, 605–606 defined, 483 expected values, 484 in multiple regression, 492 in simple linear regression, 484 Restricted models, 527 Returns adjusted closing price, 665–666 annualized, 73–74 calculating, 664 excess, 84 geometric mean, 73–74 historical, 665 mean-variance analysis, 83–84 nominal, 666 portfolio, 162–164 real, 666 risk and, 83–84, 162 risk-adjusted, 519 Sharpe ratio, 83–84 Right-tailed hypothesis, 303, 314 Right-tailed test, 412 Risk measures, 376 portfolio, 164 returns and, 83–84, 162 Risk aversion, 159–160 Risk loving consumers, 160 Risk neutral consumers, 160 Risk-adjusted returns, 519 Roche, Jehanne-Marie, 664, 674 Roosevelt, Franklin D., 232, 233 Rules of probability; see Probability rules Runs above and below median, 716–718 defined, 715 Wald-Wolfowitz runs test, 715–716 S s chart, 252 Sample coefficient of variation, 80 Sample correlation coefficient, 93, 479 Sample covariance, 92, 478 Sample mean; see also Sampling distribution of sample mean differences between, 340 formula, 60 weighted, 90 Sample mean absolute deviation, 78 Sample proportion, 360; see also Sampling distribution of sample proportion Sample regression equation multiple regression, 492–493 simple linear regression, 485–486 Sample spaces, 108; see also Events Sample standard deviation, 79 Sample statistics defined, 5, 232 estimators, 237 mean as, 61 random, 237 use of, 6, 232 Sample variance formula, 79 properties, 376 sampling distribution of, 376–377 sampling distribution of ratio of, 385 Samples defined, 5, 232 independent random, 340 matched-pairs mean difference, 351–355 INDEX jag20557_index_I1-I22.indd B U S I N E S S S TAT I S T I C S I-9 08/07/15 2:22 pm www.downloadslide.net Samples (continued) recognizing, 351 population and, 6, 232 representative of population, 232 sizes, 234, 287–289 Sampling acceptance, 251 bias in, 6, 232–233 cluster, 235 need for, 6, 232 simple random samples, 233–234 stratified, 234–235 with and without replacement, 179 Sampling distribution of sample mean central limit theorem, 240–241 defined, 237 expected values, 238 hypothesis testing, 307 normal distribution, 239–240 standard deviation, 238 variance, 238 Sampling distribution of sample proportion central limit theorem, 245 defined, 244 expected values, 244 finite population correction factor, 249 standard deviation, 244–246 variance, 244 Sampling distribution of sample variance, 376–377 Scatterplots, 43–46, 478, 486–488 Seasonal dummy variables, 640, 645–647 Seasonal indices adjusted, 642–643 unadjusted, 642 Seasonal patterns, 626 Seasonality, extracting, 641–643 Seasonally adjusted series, 644 Selection bias, 233 Semi-log model, 569, 571 Serial correlation, 537 Seton Hall University, 589, 603 Sharpe, William, 83 Sharpe ratio, 83–84 Shewhart, Walter A., 252 Sign test, 711–713 test statistic, 712 Significance levels, 309 Significance tests of dummies, 592, 600 of individual significance, 516–519 of interaction variables, 600 of joint significance, 521–522 Simple linear regression model; see also Regression analysis assumptions, 484, 537–538 defined, 485 explanatory variables, 483 goodness-of-fit tests, 497–500 I-10 jag20557_index_I1-I22.indd 10 B U S I N E S S S TAT I S T I C S response variable, 483 sample regression equation, 485–486 scatterplots, 486–488 Simple price indices, 668 Simple random samples, 233–234 Skewed distributions, 31 Skewness coefficients, 66, 419 Smoothing techniques exponential, 628–631 moving average methods, 626–628, 631 uses of, 626 Spearman rank correlation test, 705–708 Spurious correlation, 5, 481 SSA; see Sum of squares for factor A SSAB; see Sum of squares for interaction of factor A and factor B SSB; see Sum of squares for factor B SSE; see Error sum of squares SSR; see Sum of squares due to regression SST; see Total sum of squares SSTR; see Sum of squares due to treatments Standard & Poor’s 500 Index, 506 Standard deviation Chebyshev’s theorem, 85–86, 87 defined, 78 of discrete random variable, 158 empirical rule, 86–87 interpreting, 85 population, 79 of portfolio returns, 164 sample, 79 z-score, 87–88 Standard error, of sample proportion, 244 Standard error of the estimate, 497–500 Standard normal distribution defined, 198 inverse transformation, 207–209 transformation, 205–207 z values, 198–202 Standard normal table, 198 Standardizing, data, 87 Starbucks Corp., 4, 151, 177, 231, 241, 246, 247, 339, 353–354, 356 Statistical quality control; see also Control charts acceptance sampling, 251 defined, 251 detection approach, 251 population variance used in, 376 sources of variation, 251–252 Statistical software; see Excel Statistics; see also Sample statistics descriptive, importance, 4–5 inferential, Stem-and-leaf diagrams, 41–43 Stocks; see also Returns adjusted closing price, 665–666 Dow Jones Industrial Average, Stratified random sampling, 234–235 INDEX 08/07/15 2:22 pm www.downloadslide.net Studentized range table, 445 Student’s t distribution; see t distribution Study habits, hypothesis tests, 301, 322 Subjective probability, 111, 113 Sum of squares due to regression (SSR), 501 Sum of squares due to treatments (SSTR), 435 Sum of squares for factor A (SSA), 452, 459 Sum of squares for factor B (SSB), 452, 459 Sum of squares for interaction of factor A and factor B (SSAB), 459–460 Surveys, 5, 231 of tween preferences, 3, 13 Symmetric distributions, 31, 66, 86, 196; see also Normal distribution Systematic patterns, 626 T t distribution characteristics, 278 defined, 277 degrees of freedom, 278 hypothesis testing, 319–322 t test assumptions, 688 two-tailed, 517–519 Test of independence, 410–414 Test statistics for differences in means, 343 goodness-of-fit, 404–408 Jarque-Bera, 419 for Kruskal-Wallis test, 702 for mean difference, 353 for one-way ANOVA, 436 for population correlation coefficient, 480 of population mean, with known standard deviation, 308 for population proportion, 326 for population variance, 380 for population variance ratio, 389 for proportion differences, 362 for sign test, 712 for test of independence, 412 test of joint significance, 521 for test of linear restrictions, 528 for Wald-Wolfowitz runs test, 716 for Wilcoxon rank-sum test, 697 for Wilcoxon signed-rank test, 690 Thomsen, Jaqueline, 613 Time series data; see also Forecasting; Returns; Smoothing techniques defined, 6, 7, 624 deflated, 676–678 nominal terms, 676 real terms, 676 systematic patterns, 626 unsystematic patterns, 626 Total probability rules, 131–134, 136 Total sum of squares (SST), 437, 459, 500 Transformations; see also Logarithms; Polynomial regression models inverse, 207–209 normal, 205–207 Trend models exponential, 634–637 linear, 633–634, 645 polynomial, 637–638 quadratic, 637–638 Trendlines, 486–488 Trends extracting, 643–644 systematic patterns, 626 True zero point, 12 Tukey, John, 41, 442 Tukey’s honestly significant differences (HSD) method, 442, 444–446, 455 Two-tailed hypothesis, 303–305, 314, 315–316 Two-tailed t test, 517–519 Two-way ANOVA defined, 450 with interaction, 458–461 randomized block designs, 451 sample sizes, 451 uses of, 450 without interaction, 450–455 Type I error, 305–306 Type II error, 305–306 U UCL; see Upper control limit “Ultra-green” car, 269, 289 Unadjusted seasonal index, 642 Unbalanced data, 444 Unconditional probability, 120, 134 Under Armour Inc., 107, 126, 127, 128, 403, 411, 414 Unexplained variation, 500 Union, of events, 109, 110, 117 University of Pennsylvania Medical Center, Unrestricted models, 527 Unsystematic patterns, 626 Unweighted aggregate price indices, 670–671 Upper control limit (UCL), 252–253 U.S Bureau of Labor Statistics, 6, 7, 677 U.S Census Bureau, 7, 61 USA TODAY, V Vanguard, 59, 81, 375, 391, 506, 687, 709 Variability measures; see Dispersion measures Variables; see also Dummy variables; Qualitative variables; Quantitative variables continuous, defined, discrete, 8–9 response, 483, 492 INDEX jag20557_index_I1-I22.indd 11 B U S I N E S S S TAT I S T I C S I-11 08/07/15 2:22 pm www.downloadslide.net Variance; see also Analysis of variance; Population variance; Sample variance defined, 78 of discrete random variable, 158 for frequency distribution, 89–91 mean-variance analysis, 83–84 of portfolio returns, 163–164 Venn, John, 109 Venn diagrams, 109, 110 W Wald-Wolfowitz runs test, 715–718 The Wall Street Journal, Websites, data sources, Weighted aggregate price index, 671–673 Weighted mean, 66, 90 Width, confidence intervals, 273–274 Wilcoxon rank-sum test for independent samples, 693, 695–697 for matched-pairs sample, 694–695 test statistic, 697 uses of, 346, 355 Wilcoxon signed-rank test critical values, 690 for matched-pairs sample, 694–695 I-12 jag20557_index_I1-I22.indd 12 B U S I N E S S S TAT I S T I C S for population median, 688–692 software, 698 test statistic, 690 Within-treatments estimate of population variance, 435, 436–437 Within-treatments variance, 435 X X2 distribution; see Chi-square distribution _ x charts, 252 Y Yields; see Returns Z z table, 198 z values defined, 198 finding for given probability, 201–202 finding probabilities for, 198–200 inverse transformation, 207–209 normal transformation, 205–207 zillow.com, z-score, 87–88 INDEX 08/07/15 2:22 pm ... timely applications with statistical methods, students learn to appreciate the relevance of business statistics in our world today We wrote Business Statistics: Communicating with Numbers because... 1960  Business statistics: communicating with numbers / Sanjiv Jaggia,   California Polytechnic State University, Alison Kelly, Suffolk University   Second Edition   pages cm.— (Business statistics) ... Massachusetts, with her husband and two children vi jag20557_fm_i-xxxii_1.indd 29/06/15 2:43 PM A Unique Emphasis on Communicating with Numbers Makes Business Statistics Relevant to Students Statistics